Lindemann–Weierstrass theorem precursor

E113531

mathematical theorem result in transcendental number theory

The Lindemann–Weierstrass theorem precursor is an early foundational result in transcendental number theory developed by Ferdinand von Lindemann that paved the way for the full Lindemann–Weierstrass theorem on the algebraic independence of exponentials of algebraic numbers.

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All labels observed (3)

Label	Occurrences
Lindemann–Weierstrass theorem	2
Lindemann–Weierstrass theorem precursor canonical	1
Sur la fonction exponentielle (proof of transcendence of e)	1

How this entity was disambiguated

This entity first appeared as the object of triple T964267 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Lindemann–Weierstrass theorem precursor
Context triple: [Ferdinand von Lindemann, knownFor, Lindemann–Weierstrass theorem precursor]

A. Gauss’s constant
Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
B. Gauss’s lemma in number theory
Gauss’s lemma in number theory is a result that relates the Legendre symbol to the number of sign changes in a certain sequence of multiples, providing a practical criterion for determining quadratic residues modulo an odd prime.
C. Hilbert’s irreducibility theorem
Hilbert’s irreducibility theorem is a fundamental result in number theory and algebraic geometry that ensures many polynomial equations with parameterized coefficients retain irreducibility for infinitely many specializations of those parameters.
D. Weierstrass preparation theorem
The Weierstrass preparation theorem is a fundamental result in complex analysis and analytic geometry that locally expresses analytic functions near a zero as a product of a polynomial and a unit, enabling a power-series analogue of factorization.
E. Weierstrass factorization theorem
The Weierstrass factorization theorem is a fundamental result in complex analysis that expresses any entire function as an infinite product determined by its zeros, generalizing the factorization of polynomials.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Lindemann–Weierstrass theorem precursor
Target entity description: The Lindemann–Weierstrass theorem precursor is an early foundational result in transcendental number theory developed by Ferdinand von Lindemann that paved the way for the full Lindemann–Weierstrass theorem on the algebraic independence of exponentials of algebraic numbers.

A. Gauss’s constant
Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
B. Gauss’s lemma in number theory
Gauss’s lemma in number theory is a result that relates the Legendre symbol to the number of sign changes in a certain sequence of multiples, providing a practical criterion for determining quadratic residues modulo an odd prime.
C. Hilbert’s irreducibility theorem
Hilbert’s irreducibility theorem is a fundamental result in number theory and algebraic geometry that ensures many polynomial equations with parameterized coefficients retain irreducibility for infinitely many specializations of those parameters.
D. Weierstrass preparation theorem
The Weierstrass preparation theorem is a fundamental result in complex analysis and analytic geometry that locally expresses analytic functions near a zero as a product of a polynomial and a unit, enabling a power-series analogue of factorization.
E. Weierstrass factorization theorem
The Weierstrass factorization theorem is a fundamental result in complex analysis that expresses any entire function as an infinite product determined by its zeros, generalizing the factorization of polynomials.
F. None of above. chosen

Statements (11)

Predicate	Object
instanceOf	mathematical theorem ⓘ result in transcendental number theory ⓘ
areaOfApplication	theory of transcendental numbers ⓘ
author	Ferdinand von Lindemann ⓘ
consequence	development of the full Lindemann–Weierstrass theorem ⓘ
field	transcendental number theory ⓘ
influenced	later work of Karl Weierstrass on exponentials of algebraic numbers ⓘ
namedAfter	Ferdinand von Lindemann ⓘ
precedes	Lindemann–Weierstrass theorem precursor self-linksurface differs ⓘ surface form: Lindemann–Weierstrass theorem
relatedTo	Lindemann–Weierstrass theorem precursor self-linksurface differs ⓘ surface form: Lindemann–Weierstrass theorem
topic	algebraic independence of exponentials of algebraic numbers ⓘ

How these facts were elicited

Referenced by (4)

Full triples — surface form annotated when it differs from this entity's canonical label.

Ferdinand von Lindemann → knownFor → Lindemann–Weierstrass theorem precursor ⓘ

Lindemann–Weierstrass theorem precursor → relatedTo → Lindemann–Weierstrass theorem precursor self-linksurface differs ⓘ

this entity surface form: Lindemann–Weierstrass theorem

Lindemann–Weierstrass theorem precursor → precedes → Lindemann–Weierstrass theorem precursor self-linksurface differs ⓘ

this entity surface form: Lindemann–Weierstrass theorem

Charles Hermite → notableWork → Lindemann–Weierstrass theorem precursor ⓘ

this entity surface form: Sur la fonction exponentielle (proof of transcendence of e)

All labels observed (3)

How this entity was disambiguated Show

Statements (11)

How these facts were elicited Show

Referenced by (4)

How this entity was disambiguated

How these facts were elicited